numpy
2.0.0
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00001 #ifndef __NPY_MATH_C99_H_ 00002 #define __NPY_MATH_C99_H_ 00003 00004 #include <math.h> 00005 #include <numpy/npy_common.h> 00006 00007 /* 00008 * NAN and INFINITY like macros (same behavior as glibc for NAN, same as C99 00009 * for INFINITY) 00010 * 00011 * XXX: I should test whether INFINITY and NAN are available on the platform 00012 */ 00013 NPY_INLINE static float __npy_inff(void) 00014 { 00015 const union { npy_uint32 __i; float __f;} __bint = {0x7f800000UL}; 00016 return __bint.__f; 00017 } 00018 00019 NPY_INLINE static float __npy_nanf(void) 00020 { 00021 const union { npy_uint32 __i; float __f;} __bint = {0x7fc00000UL}; 00022 return __bint.__f; 00023 } 00024 00025 NPY_INLINE static float __npy_pzerof(void) 00026 { 00027 const union { npy_uint32 __i; float __f;} __bint = {0x00000000UL}; 00028 return __bint.__f; 00029 } 00030 00031 NPY_INLINE static float __npy_nzerof(void) 00032 { 00033 const union { npy_uint32 __i; float __f;} __bint = {0x80000000UL}; 00034 return __bint.__f; 00035 } 00036 00037 #define NPY_INFINITYF __npy_inff() 00038 #define NPY_NANF __npy_nanf() 00039 #define NPY_PZEROF __npy_pzerof() 00040 #define NPY_NZEROF __npy_nzerof() 00041 00042 #define NPY_INFINITY ((npy_double)NPY_INFINITYF) 00043 #define NPY_NAN ((npy_double)NPY_NANF) 00044 #define NPY_PZERO ((npy_double)NPY_PZEROF) 00045 #define NPY_NZERO ((npy_double)NPY_NZEROF) 00046 00047 #define NPY_INFINITYL ((npy_longdouble)NPY_INFINITYF) 00048 #define NPY_NANL ((npy_longdouble)NPY_NANF) 00049 #define NPY_PZEROL ((npy_longdouble)NPY_PZEROF) 00050 #define NPY_NZEROL ((npy_longdouble)NPY_NZEROF) 00051 00052 /* 00053 * Useful constants 00054 */ 00055 #define NPY_E 2.718281828459045235360287471352662498 /* e */ 00056 #define NPY_LOG2E 1.442695040888963407359924681001892137 /* log_2 e */ 00057 #define NPY_LOG10E 0.434294481903251827651128918916605082 /* log_10 e */ 00058 #define NPY_LOGE2 0.693147180559945309417232121458176568 /* log_e 2 */ 00059 #define NPY_LOGE10 2.302585092994045684017991454684364208 /* log_e 10 */ 00060 #define NPY_PI 3.141592653589793238462643383279502884 /* pi */ 00061 #define NPY_PI_2 1.570796326794896619231321691639751442 /* pi/2 */ 00062 #define NPY_PI_4 0.785398163397448309615660845819875721 /* pi/4 */ 00063 #define NPY_1_PI 0.318309886183790671537767526745028724 /* 1/pi */ 00064 #define NPY_2_PI 0.636619772367581343075535053490057448 /* 2/pi */ 00065 #define NPY_EULER 0.577215664901532860606512090082402431 /* Euler constant */ 00066 #define NPY_SQRT2 1.414213562373095048801688724209698079 /* sqrt(2) */ 00067 #define NPY_SQRT1_2 0.707106781186547524400844362104849039 /* 1/sqrt(2) */ 00068 00069 #define NPY_Ef 2.718281828459045235360287471352662498F /* e */ 00070 #define NPY_LOG2Ef 1.442695040888963407359924681001892137F /* log_2 e */ 00071 #define NPY_LOG10Ef 0.434294481903251827651128918916605082F /* log_10 e */ 00072 #define NPY_LOGE2f 0.693147180559945309417232121458176568F /* log_e 2 */ 00073 #define NPY_LOGE10f 2.302585092994045684017991454684364208F /* log_e 10 */ 00074 #define NPY_PIf 3.141592653589793238462643383279502884F /* pi */ 00075 #define NPY_PI_2f 1.570796326794896619231321691639751442F /* pi/2 */ 00076 #define NPY_PI_4f 0.785398163397448309615660845819875721F /* pi/4 */ 00077 #define NPY_1_PIf 0.318309886183790671537767526745028724F /* 1/pi */ 00078 #define NPY_2_PIf 0.636619772367581343075535053490057448F /* 2/pi */ 00079 #define NPY_EULERf 0.577215664901532860606512090082402431F /* Euler constan*/ 00080 #define NPY_SQRT2f 1.414213562373095048801688724209698079F /* sqrt(2) */ 00081 #define NPY_SQRT1_2f 0.707106781186547524400844362104849039F /* 1/sqrt(2) */ 00082 00083 #define NPY_El 2.718281828459045235360287471352662498L /* e */ 00084 #define NPY_LOG2El 1.442695040888963407359924681001892137L /* log_2 e */ 00085 #define NPY_LOG10El 0.434294481903251827651128918916605082L /* log_10 e */ 00086 #define NPY_LOGE2l 0.693147180559945309417232121458176568L /* log_e 2 */ 00087 #define NPY_LOGE10l 2.302585092994045684017991454684364208L /* log_e 10 */ 00088 #define NPY_PIl 3.141592653589793238462643383279502884L /* pi */ 00089 #define NPY_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */ 00090 #define NPY_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */ 00091 #define NPY_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */ 00092 #define NPY_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */ 00093 #define NPY_EULERl 0.577215664901532860606512090082402431L /* Euler constan*/ 00094 #define NPY_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */ 00095 #define NPY_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */ 00096 00097 /* 00098 * C99 double math funcs 00099 */ 00100 double npy_sin(double x); 00101 double npy_cos(double x); 00102 double npy_tan(double x); 00103 double npy_sinh(double x); 00104 double npy_cosh(double x); 00105 double npy_tanh(double x); 00106 00107 double npy_asin(double x); 00108 double npy_acos(double x); 00109 double npy_atan(double x); 00110 double npy_aexp(double x); 00111 double npy_alog(double x); 00112 double npy_asqrt(double x); 00113 double npy_afabs(double x); 00114 00115 double npy_log(double x); 00116 double npy_log10(double x); 00117 double npy_exp(double x); 00118 double npy_sqrt(double x); 00119 00120 double npy_fabs(double x); 00121 double npy_ceil(double x); 00122 double npy_fmod(double x, double y); 00123 double npy_floor(double x); 00124 00125 double npy_expm1(double x); 00126 double npy_log1p(double x); 00127 double npy_hypot(double x, double y); 00128 double npy_acosh(double x); 00129 double npy_asinh(double xx); 00130 double npy_atanh(double x); 00131 double npy_rint(double x); 00132 double npy_trunc(double x); 00133 double npy_exp2(double x); 00134 double npy_log2(double x); 00135 00136 double npy_atan2(double x, double y); 00137 double npy_pow(double x, double y); 00138 double npy_modf(double x, double* y); 00139 00140 double npy_copysign(double x, double y); 00141 double npy_nextafter(double x, double y); 00142 double npy_spacing(double x); 00143 00144 /* 00145 * IEEE 754 fpu handling. Those are guaranteed to be macros 00146 */ 00147 #ifndef NPY_HAVE_DECL_ISNAN 00148 #define npy_isnan(x) ((x) != (x)) 00149 #else 00150 #ifdef _MSC_VER 00151 #define npy_isnan(x) _isnan((x)) 00152 #else 00153 #define npy_isnan(x) isnan((x)) 00154 #endif 00155 #endif 00156 00157 #ifndef NPY_HAVE_DECL_ISFINITE 00158 #ifdef _MSC_VER 00159 #define npy_isfinite(x) _finite((x)) 00160 #else 00161 #define npy_isfinite(x) !npy_isnan((x) + (-x)) 00162 #endif 00163 #else 00164 #define npy_isfinite(x) isfinite((x)) 00165 #endif 00166 00167 #ifndef NPY_HAVE_DECL_ISINF 00168 #define npy_isinf(x) (!npy_isfinite(x) && !npy_isnan(x)) 00169 #else 00170 #ifdef _MSC_VER 00171 #define npy_isinf(x) (!_finite((x)) && !_isnan((x))) 00172 #else 00173 #define npy_isinf(x) isinf((x)) 00174 #endif 00175 #endif 00176 00177 #ifndef NPY_HAVE_DECL_SIGNBIT 00178 int _npy_signbit_f(float x); 00179 int _npy_signbit_d(double x); 00180 int _npy_signbit_ld(long double x); 00181 #define npy_signbit(x) \ 00182 (sizeof (x) == sizeof (long double) ? _npy_signbit_ld (x) \ 00183 : sizeof (x) == sizeof (double) ? _npy_signbit_d (x) \ 00184 : _npy_signbit_f (x)) 00185 #else 00186 #define npy_signbit(x) signbit((x)) 00187 #endif 00188 00189 /* 00190 * float C99 math functions 00191 */ 00192 00193 float npy_sinf(float x); 00194 float npy_cosf(float x); 00195 float npy_tanf(float x); 00196 float npy_sinhf(float x); 00197 float npy_coshf(float x); 00198 float npy_tanhf(float x); 00199 float npy_fabsf(float x); 00200 float npy_floorf(float x); 00201 float npy_ceilf(float x); 00202 float npy_rintf(float x); 00203 float npy_truncf(float x); 00204 float npy_sqrtf(float x); 00205 float npy_log10f(float x); 00206 float npy_logf(float x); 00207 float npy_expf(float x); 00208 float npy_expm1f(float x); 00209 float npy_asinf(float x); 00210 float npy_acosf(float x); 00211 float npy_atanf(float x); 00212 float npy_asinhf(float x); 00213 float npy_acoshf(float x); 00214 float npy_atanhf(float x); 00215 float npy_log1pf(float x); 00216 float npy_exp2f(float x); 00217 float npy_log2f(float x); 00218 00219 float npy_atan2f(float x, float y); 00220 float npy_hypotf(float x, float y); 00221 float npy_powf(float x, float y); 00222 float npy_fmodf(float x, float y); 00223 00224 float npy_modff(float x, float* y); 00225 00226 float npy_copysignf(float x, float y); 00227 float npy_nextafterf(float x, float y); 00228 float npy_spacingf(float x); 00229 00230 /* 00231 * float C99 math functions 00232 */ 00233 00234 npy_longdouble npy_sinl(npy_longdouble x); 00235 npy_longdouble npy_cosl(npy_longdouble x); 00236 npy_longdouble npy_tanl(npy_longdouble x); 00237 npy_longdouble npy_sinhl(npy_longdouble x); 00238 npy_longdouble npy_coshl(npy_longdouble x); 00239 npy_longdouble npy_tanhl(npy_longdouble x); 00240 npy_longdouble npy_fabsl(npy_longdouble x); 00241 npy_longdouble npy_floorl(npy_longdouble x); 00242 npy_longdouble npy_ceill(npy_longdouble x); 00243 npy_longdouble npy_rintl(npy_longdouble x); 00244 npy_longdouble npy_truncl(npy_longdouble x); 00245 npy_longdouble npy_sqrtl(npy_longdouble x); 00246 npy_longdouble npy_log10l(npy_longdouble x); 00247 npy_longdouble npy_logl(npy_longdouble x); 00248 npy_longdouble npy_expl(npy_longdouble x); 00249 npy_longdouble npy_expm1l(npy_longdouble x); 00250 npy_longdouble npy_asinl(npy_longdouble x); 00251 npy_longdouble npy_acosl(npy_longdouble x); 00252 npy_longdouble npy_atanl(npy_longdouble x); 00253 npy_longdouble npy_asinhl(npy_longdouble x); 00254 npy_longdouble npy_acoshl(npy_longdouble x); 00255 npy_longdouble npy_atanhl(npy_longdouble x); 00256 npy_longdouble npy_log1pl(npy_longdouble x); 00257 npy_longdouble npy_exp2l(npy_longdouble x); 00258 npy_longdouble npy_log2l(npy_longdouble x); 00259 00260 npy_longdouble npy_atan2l(npy_longdouble x, npy_longdouble y); 00261 npy_longdouble npy_hypotl(npy_longdouble x, npy_longdouble y); 00262 npy_longdouble npy_powl(npy_longdouble x, npy_longdouble y); 00263 npy_longdouble npy_fmodl(npy_longdouble x, npy_longdouble y); 00264 00265 npy_longdouble npy_modfl(npy_longdouble x, npy_longdouble* y); 00266 00267 npy_longdouble npy_copysignl(npy_longdouble x, npy_longdouble y); 00268 npy_longdouble npy_nextafterl(npy_longdouble x, npy_longdouble y); 00269 npy_longdouble npy_spacingl(npy_longdouble x); 00270 00271 /* 00272 * Non standard functions 00273 */ 00274 double npy_deg2rad(double x); 00275 double npy_rad2deg(double x); 00276 double npy_logaddexp(double x, double y); 00277 double npy_logaddexp2(double x, double y); 00278 00279 float npy_deg2radf(float x); 00280 float npy_rad2degf(float x); 00281 float npy_logaddexpf(float x, float y); 00282 float npy_logaddexp2f(float x, float y); 00283 00284 npy_longdouble npy_deg2radl(npy_longdouble x); 00285 npy_longdouble npy_rad2degl(npy_longdouble x); 00286 npy_longdouble npy_logaddexpl(npy_longdouble x, npy_longdouble y); 00287 npy_longdouble npy_logaddexp2l(npy_longdouble x, npy_longdouble y); 00288 00289 #define npy_degrees npy_rad2deg 00290 #define npy_degreesf npy_rad2degf 00291 #define npy_degreesl npy_rad2degl 00292 00293 #define npy_radians npy_deg2rad 00294 #define npy_radiansf npy_deg2radf 00295 #define npy_radiansl npy_deg2radl 00296 00297 /* 00298 * Complex declarations 00299 */ 00300 00301 /* 00302 * C99 specifies that complex numbers have the same representation as 00303 * an array of two elements, where the first element is the real part 00304 * and the second element is the imaginary part. 00305 */ 00306 #define __NPY_CPACK_IMP(x, y, type, ctype) \ 00307 union { \ 00308 ctype z; \ 00309 type a[2]; \ 00310 } z1;; \ 00311 \ 00312 z1.a[0] = (x); \ 00313 z1.a[1] = (y); \ 00314 \ 00315 return z1.z; 00316 00317 static NPY_INLINE npy_cdouble npy_cpack(double x, double y) 00318 { 00319 __NPY_CPACK_IMP(x, y, double, npy_cdouble); 00320 } 00321 00322 static NPY_INLINE npy_cfloat npy_cpackf(float x, float y) 00323 { 00324 __NPY_CPACK_IMP(x, y, float, npy_cfloat); 00325 } 00326 00327 static NPY_INLINE npy_clongdouble npy_cpackl(npy_longdouble x, npy_longdouble y) 00328 { 00329 __NPY_CPACK_IMP(x, y, npy_longdouble, npy_clongdouble); 00330 } 00331 #undef __NPY_CPACK_IMP 00332 00333 /* 00334 * Same remark as above, but in the other direction: extract first/second 00335 * member of complex number, assuming a C99-compatible representation 00336 * 00337 * Those are defineds as static inline, and such as a reasonable compiler would 00338 * most likely compile this to one or two instructions (on CISC at least) 00339 */ 00340 #define __NPY_CEXTRACT_IMP(z, index, type, ctype) \ 00341 union { \ 00342 ctype z; \ 00343 type a[2]; \ 00344 } __z_repr; \ 00345 __z_repr.z = z; \ 00346 \ 00347 return __z_repr.a[index]; 00348 00349 static NPY_INLINE double npy_creal(npy_cdouble z) 00350 { 00351 __NPY_CEXTRACT_IMP(z, 0, double, npy_cdouble); 00352 } 00353 00354 static NPY_INLINE double npy_cimag(npy_cdouble z) 00355 { 00356 __NPY_CEXTRACT_IMP(z, 1, double, npy_cdouble); 00357 } 00358 00359 static NPY_INLINE float npy_crealf(npy_cfloat z) 00360 { 00361 __NPY_CEXTRACT_IMP(z, 0, float, npy_cfloat); 00362 } 00363 00364 static NPY_INLINE float npy_cimagf(npy_cfloat z) 00365 { 00366 __NPY_CEXTRACT_IMP(z, 1, float, npy_cfloat); 00367 } 00368 00369 static NPY_INLINE npy_longdouble npy_creall(npy_clongdouble z) 00370 { 00371 __NPY_CEXTRACT_IMP(z, 0, npy_longdouble, npy_clongdouble); 00372 } 00373 00374 static NPY_INLINE npy_longdouble npy_cimagl(npy_clongdouble z) 00375 { 00376 __NPY_CEXTRACT_IMP(z, 1, npy_longdouble, npy_clongdouble); 00377 } 00378 #undef __NPY_CEXTRACT_IMP 00379 00380 /* 00381 * Double precision complex functions 00382 */ 00383 double npy_cabs(npy_cdouble z); 00384 double npy_carg(npy_cdouble z); 00385 00386 npy_cdouble npy_cexp(npy_cdouble z); 00387 npy_cdouble npy_clog(npy_cdouble z); 00388 npy_cdouble npy_cpow(npy_cdouble x, npy_cdouble y); 00389 00390 npy_cdouble npy_csqrt(npy_cdouble z); 00391 00392 npy_cdouble npy_ccos(npy_cdouble z); 00393 npy_cdouble npy_csin(npy_cdouble z); 00394 00395 /* 00396 * Single precision complex functions 00397 */ 00398 float npy_cabsf(npy_cfloat z); 00399 float npy_cargf(npy_cfloat z); 00400 00401 npy_cfloat npy_cexpf(npy_cfloat z); 00402 npy_cfloat npy_clogf(npy_cfloat z); 00403 npy_cfloat npy_cpowf(npy_cfloat x, npy_cfloat y); 00404 00405 npy_cfloat npy_csqrtf(npy_cfloat z); 00406 00407 npy_cfloat npy_ccosf(npy_cfloat z); 00408 npy_cfloat npy_csinf(npy_cfloat z); 00409 00410 /* 00411 * Extended precision complex functions 00412 */ 00413 npy_longdouble npy_cabsl(npy_clongdouble z); 00414 npy_longdouble npy_cargl(npy_clongdouble z); 00415 00416 npy_clongdouble npy_cexpl(npy_clongdouble z); 00417 npy_clongdouble npy_clogl(npy_clongdouble z); 00418 npy_clongdouble npy_cpowl(npy_clongdouble x, npy_clongdouble y); 00419 00420 npy_clongdouble npy_csqrtl(npy_clongdouble z); 00421 00422 npy_clongdouble npy_ccosl(npy_clongdouble z); 00423 npy_clongdouble npy_csinl(npy_clongdouble z); 00424 00425 /* 00426 * Functions that set the floating point error 00427 * status word. 00428 */ 00429 00430 void npy_set_floatstatus_divbyzero(void); 00431 void npy_set_floatstatus_overflow(void); 00432 void npy_set_floatstatus_underflow(void); 00433 void npy_set_floatstatus_invalid(void); 00434 00435 #endif